Decentralized time critical assignment is popular in the domains of military and emergency response. Considering the large communication delay, unpredictable environment and constraints, to make a rational decision in time critical context toward their common goal, agents have to jointly allocate multiple tasks based on their current status. This process can be built as a Markov Decision Model when they can share their status freely. However, it is computationally infeasible when explicit communication becomes a severe bottleneck. In this paper, by modelling the decision process as a Partially Observable Markov Decision Process for each agent and building heuristic approaches to estimate the state and reduce the action space, we apply greedy policies in our heuristic algorithms to quickly respond to time critical requirement.